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基于贝叶斯理论的非线性结构模型修正及其动力可靠度分析

丁雅杰 王佐才 辛宇 戈壁 袁子青

丁雅杰, 王佐才, 辛宇, 戈壁, 袁子青. 基于贝叶斯理论的非线性结构模型修正及其动力可靠度分析[J]. 工程力学, 2022, 39(12): 13-22, 59. doi: 10.6052/j.issn.1000-4750.2021.07.0556
引用本文: 丁雅杰, 王佐才, 辛宇, 戈壁, 袁子青. 基于贝叶斯理论的非线性结构模型修正及其动力可靠度分析[J]. 工程力学, 2022, 39(12): 13-22, 59. doi: 10.6052/j.issn.1000-4750.2021.07.0556
DING Ya-jie, WANG Zuo-cai, XIN Yu, GE Bi, YUAN Zi-qing. BAYESIAN-BASED NONLINEAR MODEL UPDATING AND DYNAMIC RELIABILITY ANALYSIS[J]. Engineering Mechanics, 2022, 39(12): 13-22, 59. doi: 10.6052/j.issn.1000-4750.2021.07.0556
Citation: DING Ya-jie, WANG Zuo-cai, XIN Yu, GE Bi, YUAN Zi-qing. BAYESIAN-BASED NONLINEAR MODEL UPDATING AND DYNAMIC RELIABILITY ANALYSIS[J]. Engineering Mechanics, 2022, 39(12): 13-22, 59. doi: 10.6052/j.issn.1000-4750.2021.07.0556

基于贝叶斯理论的非线性结构模型修正及其动力可靠度分析

doi: 10.6052/j.issn.1000-4750.2021.07.0556
基金项目: 国家自然科学基金优秀青年科学基金项目(51922036);安徽省重点研发计划项目(1804a0802204);中央高校基本科研业务费专项资金项目(JZ2020HGPB0117)
详细信息
    作者简介:

    丁雅杰(1991−),男,安徽滁州人,博士生,从事非线性结构模型修正及其参数不确定性分析研究(E-mail: dingyajie@mail.hfut.edu.cn)

    辛 宇(1991−),男,安徽蚌埠人,博士,主要从事桥梁健康监测方面研究(E-mail: 2020800133@hfut.edu.cn)

    戈 壁(1990−),男,安徽六安人,博士生,主要从事桥梁健康监测方面研究(E-mail: gebi@mail.hfut.edu.cn)

    袁子青(1997−),女,甘肃兰州人,博士生,主要从事桥梁健康监测方面研究(E-mail: 2019110605@mail.hfut.edu.cn)

    通讯作者:

    王佐才(1982−),男,湖南双峰人,教授,博士,博导,主要从事桥梁健康监测方面研究(E-mail: wangzuocai@hfut.edu.cn)

  • 中图分类号: TU311

BAYESIAN-BASED NONLINEAR MODEL UPDATING AND DYNAMIC RELIABILITY ANALYSIS

  • 摘要: 提出一种基于贝叶斯推理的非线性结构模型修正方法,同时考虑激励的随机性,建立了复合随机振动系统的动力可靠度分析方法。利用实测结构动力响应主分量的瞬时特征参数作为非线性指标构建似然函数,结合拒绝延缓自适应(Delayed Rejection and Adaptive Metropolis, DRAM)算法和高斯过程替代模型实现了非线性结构模型修正及其参数的不确定性量化。根据首次超越破坏准则,利用广义概率密度演化方法,分别对仅考虑激励随机性的确定性模型和同时考虑结构参数与激励不确定性的复合随机振动模型进行动力可靠度分析,并利用蒙特卡洛随机抽样方法验证了计算结果的准确性。研究结果表明:基于振动响应瞬时特征参数的贝叶斯推理方法能够快速、准确地实现结构的非线性模型修正及其参数的不确定性量化。与具有初始设计参数名义值的确定性模型相比,考虑参数不确定性的复合随机模型的动力可靠度总体偏低,因此,在结构安全评估中应考虑非线性模型参数不确定性的影响,使评估结果更加安全、可靠。
  • 图  1  DRAM算法流程图

    Figure  1.  Flow chart of DRAM algorithm

    图  2  五层非线性剪切模型 /m

    Figure  2.  Five-layer nonlinear shear model

    图  3  Bouc-Wen模型

    Figure  3.  Bouc-Wen model

    图  4  结构顶层的加速度响应

    Figure  4.  Acceleration response of top floor

    图  5  结构主分量瞬时特征参数

    Figure  5.  Instantaneous characteristics of principal component response

    图  6  残差正态分位图

    Figure  6.  Normal quantile-quantile plot

    图  7  参数γ的马尔科夫链

    Figure  7.  Markov chain of γ

    图  8  模拟的30次瞬时加速度幅值

    Figure  8.  30 sets of simulated instantaneous acceleration amplitudes

    图  9  参数γ的后验样本

    Figure  9.  Posterior samples of γ

    图  10  不同时刻概率分布

    Figure  10.  Probability distribution of different time

    图  11  不同时刻概率密度演化

    Figure  11.  Probability density evolution of different time

    图  12  结构顶层位移时程均值和标准差对比

    Figure  12.  Comparison of time history mean and standard deviation of top floor displacement

    图  13  不同位移界限条件下结构动力可靠度

    Figure  13.  Dynamic reliability under different displacement boundary conditions

    图  14  不同速度界限条件下结构动力可靠度

    Figure  14.  Dynamic reliability under different velocity boundary conditions

    表  1  非线性Bouc-Wen模型参数的名义值

    Table  1.   Nominal value of nonlinear Bouc-Wen model parameters

    参数 α A μ β/mμ γ/mμ
    名义值 0.4 1.0 3.0 0.5 0.5
    下载: 导出CSV

    表  2  非线性Bouc-Wen模型参数修正结果

    Table  2.   Updated results of nonlinear Bouc-Wen model parameters

    参数 名义值 DRAM MH
    后验
    均值
    变异
    系数
    样本
    接受率
    后验
    均值
    变异
    系数
    样本
    接受率
    $ \alpha $ 0.4 0.39 0.031 0.47 0.38 0.074 0.28
    A 1.0 1.02 0.012 0.39 1.05 0.038 0.11
    $ \mu $ 3.0 2.98 0.040 0.51 2.96 0.084 0.14
    $ \beta $/mμ 0.5 0.51 0.024 0.46 0.51 0.032 0.29
    $ \gamma $/mμ 0.5 0.48 0.025 0.49 0.47 0.059 0.22
    下载: 导出CSV

    表  3  非线性结构模型修正结果

    Table  3.   Updated results of nonlinear model

    参数 名义值 后验均值 变异系数 样本接受率
    $ \mit\alpha $ 0.4 0.39 0.023 0.53
    A 1.0 1.08 0.017 0.48
    $ \mit\mu $ 3.0 2.97 0.026 0.65
    $ \mit\beta $/mμ 0.5 0.52 0.037 0.44
    $ \mit\gamma $/mμ 0.5 0.49 0.031 0.57
    下载: 导出CSV

    表  4  非线性模型随机参数与激励随机参数

    Table  4.   Random parameters of nonlinear model and excitation

    随机参数分布概型均值变异系数
    $ \mit\alpha $正态分布0.390.031
    A正态分布1.020.012
    $\mit\mu $正态分布2.980.040
    $ \mit\beta $/mμ正态分布0.510.024
    $ \mit\gamma $/mμ正态分布0.480.025
    PGA/g正态分布0.200.100
    下载: 导出CSV

    表  5  不同位移界限条件下结构动力可靠度对比

    Table  5.   Dynamic reliability for different displacement boundary conditions

    界限值$ {x_{\lim }} $/m动力可靠度R(t)
    名义模型复合随机模型蒙特卡洛模拟
    0.0600.37660.29090.2946
    0.0700.88510.81630.8224
    0.0801.00000.98080.9852
    0.0851.00000.99940.9997
    0.0901.00001.00001.0000
    下载: 导出CSV

    表  6  不同速度界限条件下结构动力可靠度对比

    Table  6.   Comparison of dynamic reliability for different velocity boundary conditions

    界限值$ {\dot x_{\lim }} $/(cm/s)动力可靠度R(t)
    名义模型复合随机模型蒙特卡洛模拟
    200.41790.34530.3394
    220.78180.58410.5803
    240.94750.85120.8702
    261.00000.94750.9413
    281.00000.99970.9992
    301.00001.00001.0000
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-07-20
  • 修回日期:  2021-09-19
  • 网络出版日期:  2021-09-30
  • 刊出日期:  2022-12-01

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